Planarity of the 2-level cactus model

Sabine Cornelsen; Yefim Dinitz; Dorothea Wagner

doi:10.1007/3-540-45477-2_10

Planarity of the 2-level cactus model

Sabine Cornelsen
, Yefim Dinitz
, Dorothea Wagner

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The 2-level cactus introduced by Dinitz and Nutov in [5] is a data structure that represents the minimum and minimum+1 edge-cuts of an undirected connected multi-graph G in a compact way. In this paper, we study planarity of the 2-level cactus, which can be used, e.g., in graph drawing. We give a new sufficient planarity criterion in terms of projection paths over a spanning subtree of a graph. Using this criterion, we show that the 2-level cactus of G is planar if the cardinality of a minimum edge-cut of G is not equal to 2, 3 or 5. On the other hand, we give examples for non-planar 2-level cacti of graphs with these connectivities.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings
Editors	Andreas Brandstadt, Van Bang Le
Publisher	Springer Verlag
Pages	91-102
Number of pages	12
ISBN (Print)	3540427074, 9783540427070
DOIs	https://doi.org/10.1007/3-540-45477-2_10
State	Published - 1 Jan 2001
Event	27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001 - Boltenhagen, Germany Duration: 14 Jun 2001 → 16 Jun 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2204
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001
Country/Territory	Germany
City	Boltenhagen
Period	14/06/01 → 16/06/01

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-45477-2_10

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Cornelsen, S., Dinitz, Y., & Wagner, D. (2001). Planarity of the 2-level cactus model. In A. Brandstadt, & V. B. Le (Eds.), Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings (pp. 91-102). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2204). Springer Verlag. https://doi.org/10.1007/3-540-45477-2_10

Cornelsen, Sabine ; Dinitz, Yefim ; Wagner, Dorothea. / Planarity of the 2-level cactus model. Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. editor / Andreas Brandstadt ; Van Bang Le. Springer Verlag, 2001. pp. 91-102 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Planarity of the 2-level cactus model",

abstract = "The 2-level cactus introduced by Dinitz and Nutov in [5] is a data structure that represents the minimum and minimum+1 edge-cuts of an undirected connected multi-graph G in a compact way. In this paper, we study planarity of the 2-level cactus, which can be used, e.g., in graph drawing. We give a new sufficient planarity criterion in terms of projection paths over a spanning subtree of a graph. Using this criterion, we show that the 2-level cactus of G is planar if the cardinality of a minimum edge-cut of G is not equal to 2, 3 or 5. On the other hand, we give examples for non-planar 2-level cacti of graphs with these connectivities.",

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Cornelsen, S, Dinitz, Y & Wagner, D 2001, Planarity of the 2-level cactus model. in A Brandstadt & VB Le (eds), Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2204, Springer Verlag, pp. 91-102, 27th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2001, Boltenhagen, Germany, 14/06/01. https://doi.org/10.1007/3-540-45477-2_10

Planarity of the 2-level cactus model. / Cornelsen, Sabine; Dinitz, Yefim; Wagner, Dorothea.
Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. ed. / Andreas Brandstadt; Van Bang Le. Springer Verlag, 2001. p. 91-102 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2204).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Planarity of the 2-level cactus model

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N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2001.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - The 2-level cactus introduced by Dinitz and Nutov in [5] is a data structure that represents the minimum and minimum+1 edge-cuts of an undirected connected multi-graph G in a compact way. In this paper, we study planarity of the 2-level cactus, which can be used, e.g., in graph drawing. We give a new sufficient planarity criterion in terms of projection paths over a spanning subtree of a graph. Using this criterion, we show that the 2-level cactus of G is planar if the cardinality of a minimum edge-cut of G is not equal to 2, 3 or 5. On the other hand, we give examples for non-planar 2-level cacti of graphs with these connectivities.

AB - The 2-level cactus introduced by Dinitz and Nutov in [5] is a data structure that represents the minimum and minimum+1 edge-cuts of an undirected connected multi-graph G in a compact way. In this paper, we study planarity of the 2-level cactus, which can be used, e.g., in graph drawing. We give a new sufficient planarity criterion in terms of projection paths over a spanning subtree of a graph. Using this criterion, we show that the 2-level cactus of G is planar if the cardinality of a minimum edge-cut of G is not equal to 2, 3 or 5. On the other hand, we give examples for non-planar 2-level cacti of graphs with these connectivities.

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Cornelsen S, Dinitz Y, Wagner D. Planarity of the 2-level cactus model. In Brandstadt A, Le VB, editors, Graph-Theoretic Concepts in Computer Science - 27th International Workshop, WG 2001, Proceedings. Springer Verlag. 2001. p. 91-102. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45477-2_10

Planarity of the 2-level cactus model

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